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l'enseignement de l'espace et de la géométrie dans la scolarité obligatoire

Abstract : In the french curriculum, the teaching of spatial knowings does'nt exists any more since the second year of primary school ; the teaching of geometry elementary figures substitutes it. That choice leave children and adults powerless in a lot of common life or professional situations.needing theproduction or the use of spatial representations Elsewhere, the teaching of geometry in the middle school constitue an obstacle to the learning of mathematics for too many pupils.
This thesis is a study of the links between this double phenomena, and an attempt to propose solutions.
The study shows how the didactical contract of the teaching process of geometry leans on on the cultrual fiction of the transparence of spatial relations with space in the learning of the elementary geometry ; the pupils have to constitute and to make use the knowings which are necessary to understand the teached geometry ; whereas these knowings ar'nt naturally acquired in our society by usual interactions with spatial environment ; so in case of learning failure, this fiction only allows the teacher to do inefficient remediations or/and to transfer its responsability to the pupil.
The theoretical study leans upon the theory of situations developped by G Brousseau.
The authors propose to distinguish three main kind of relation with space called problematics : the practical problematic, the problematic of spatio-geometrical modelisation, the geometrical problematic (deductive or theorical). They show by numerous samples how the the teaching process without considering these problematics and their articulation constutute the them as obstacles to the learning process
In order to construct teaching situations allowing the overtaking these obstacles, the authors resume and extend the three analysis of the spatial representations inroducted by G. Galvez and G Brousseau : micro, meso, and macro spaces.
This study brings several experimental teaching processes, upon drawing and using plans of meso and macro space since elementary school, upon angles and their measure at the end of elementary school, upon introduction of reasoning about elementary figures, and a comparison study between several situations proposed to introduce the demonstration in the middle school.
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Contributor : René Berthelot <>
Submitted on : Monday, September 7, 2009 - 4:53:56 PM
Last modification on : Wednesday, November 29, 2017 - 2:54:04 PM
Long-term archiving on: : Tuesday, June 15, 2010 - 11:18:17 PM


  • HAL Id : tel-00414065, version 1



René Berthelot, Marie Hélène Salin. l'enseignement de l'espace et de la géométrie dans la scolarité obligatoire. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 1992. Français. ⟨tel-00414065⟩



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